How to make xcalib always start up automatically?

Well, a simple solution would be to first let the system write the settings and then overwrite them yourself ;)

So, you should add to your command a timeout at first, so as to let the system do what it has to do, and then you should overwrite these settings. This should be your command:

bash -c 'sleep 10 && xcalib -gc 1.2 monitor-profile.icc'

This will wait 10 seconds at first (you may need to tweak this timeout so as to much your needs) and then it will execute your command.

As a result, you will overwrite what the system has written and not vice versa.